Implementation of the RCIP scheme and its performance for 1-D age computations in ice-sheet models

Abstract

Ice-sheet age computations are formulated using an Eulerian advection equation, and there are many schemes that can be used to solve them numerically. Typically, these differ in numerical characteristics such as stability, accuracy, and diffusivity. Furthermore, although various methods have been presented for ice-sheet age computations, the constrained interpolation profile method and its variants have not been examined in this context. The present study introduces one of its variants, a rational function-based constrained interpolation profile (RCIP) scheme, to one-dimensional ice age computation and demonstrates its performance levels via comparisons with those obtained from first- and second-order upwind schemes. Our results show that the RCIP scheme preserves the pattern of input surface mass balance histories in terms of the vertical profile of internal annual layer thickness better than the other schemes.